New answers tagged stochastic-volatility
2
The Heston model can have that property. If you make the correlation negative between the Brownian motions in the $dS_{t}$ process and the $d\nu_{t}$ process you imply that price is negatively correlated with variance.
1
Yeah this is often called Spot-Vol correlation and is well known. Most people take this into account. I think if you just google spot-vol correlation you will come up with many example/models.
1
Apologies for the delay on the hedging of non-forward-starting volatility swaps, but it's only since this week that I have an answer for this.
So, for plain volswaps, I can give you a nonparametric hedge in terms of varswaps only. That's not as cheap as using a single option (which I believe is not possibe anyway), but certainly better than trading an ...
7
I've seen that Gordon answer is more concise and to the point. Take this as a complementary answer.
This is a general approach that will work for all this type of linear SDEs, not just this one. Assume we have the following linear SDE
$$dX_t = (F_t X_t +f_t)dt + (G_t X_t +g_t)dB_t \tag*{(1)}$$
where $F, G, f$ and $g$ are Borel measurable bounded ...
10
Let
\begin{align*}
Y_t = e^{(a+\frac{c^2}{2})t-cW_t}.
\end{align*}
Then
\begin{align*}
dY_t = Y_t\left[\big(a+c^2\big)dt -c dW_t \right].
\end{align*}
Moreover,
\begin{align*}
d(X_tY_t) &= Y_t dX_t + X_t dY_t + d\langle X, Y\rangle_t\\
&=abY_tdt.
\end{align*}
That is,
\begin{align*}
X_t = Y_t^{-1}\left(X_0 + ab\int_0^t Y_sds\right).
\end{align*}
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